Solve x+1/x-5=x+9/x+7

$$\frac { x + 1 } { x - 5 } = \frac { x + 9 } { x + 7 }$$

Solve for x

$$x=-13$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -7,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x+7\right), the least common multiple of x-5,x+7.

$$\left(x+7\right)\left(x+1\right)=\left(x-5\right)\left(x+9\right)$$

Use the distributive property to multiply x+7 by x+1 and combine like terms.

$$x^{2}+8x+7=\left(x-5\right)\left(x+9\right)$$

Use the distributive property to multiply x-5 by x+9 and combine like terms.

$$x^{2}+8x+7=x^{2}+4x-45$$

Subtract x^{2} from both sides.

$$x^{2}+8x+7-x^{2}=4x-45$$

Combine x^{2} and -x^{2} to get 0.

$$8x+7=4x-45$$

Subtract 4x from both sides.

$$8x+7-4x=-45$$

Combine 8x and -4x to get 4x.

$$4x+7=-45$$

Subtract 7 from both sides.

$$4x=-45-7$$

Subtract 7 from -45 to get -52.

$$4x=-52$$

Divide both sides by 4.

$$x=\frac{-52}{4}$$

Divide -52 by 4 to get -13.

$$x=-13$$